If x + y + z = 0 and x2 + y2 + z2 = 12, then the value of |xy + yz + zx| is ___
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x^2 + y^2 +z^2 = 12 --------(1)
x + y + z = 0
On squaring both sides, we get
x^2 + y^2 + z^2 + 2xy + 2yz + 2zx = 0
=> 12 + 2 ( xy + yz + zx) = 0 [ using equation 1]
=> 2 ( xy + yz + zx) = - 12
=> xy + yz + zx = - 6
=> | xy + yz + zx | = 6
x + y + z = 0
On squaring both sides, we get
x^2 + y^2 + z^2 + 2xy + 2yz + 2zx = 0
=> 12 + 2 ( xy + yz + zx) = 0 [ using equation 1]
=> 2 ( xy + yz + zx) = - 12
=> xy + yz + zx = - 6
=> | xy + yz + zx | = 6
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